Chapter 2, Problem 94E

The energy of a vibrating molecule is quantized much like the energy of an electron in the hydrogen atom. The energy levels of a vibrating molecule are given by the equation $E_n=\left(n+\frac{1}{2}\right)hv$ where n is a quantum number with possible values of 1,2,..., and v is the frequency of vibration. The vibration frequency of HCI is approximately $8.85\times {10}^{13}{s}^{-1}$ . What minimum energy is required to excite a vibration in HCI? What wavelength of light is required to excite this vibration?